189 An in vitro model of fibrosis using crosslinked native extracellular matrix-derived hydrogels to modulate biomechanics without changing composition Characterization of the Mechanical properties Both LdECM and Ru-LdECM hydrogels were made as described in hydrogel preparation. The gels were subjected to uniaxial compression with a 2.5 mm diameter plunger at three different locations, at least 2 mm away from the gel border and ensuring 2 mm or more between each compression site (Figure 1C). The stress relaxation test was performed with a low-load compression tester (LLCT) at RT as described previously [6, 26, 29]. The LabVIEW 7.1 program was used for the LLCT load cell and linear positioning for control and data acquisition. The resolution in position, load, and time determination was 0.001 mm, 2 mg, and 25 ms, respectively, and the compression speed was controlled in feedback mode. Samples were compressed to 20% of their original thickness (strain ε = 0.2) at a deformation speed of 20 %/s (strain rate ε̇ = 0.2 s−1). The deformation was held constant for 100 s and the stress continuously monitored. During compression, the required stress was plotted against the strain. In this plot, a linear increase in stress as a function of strain was observed between a strain of 0.04 and 0.1; the slope of the line fit to this region was taken as Young’s modulus. Young’s modulus essentially describes the stiffness of a material [30]. Since the Young’s modulus of the viscoelastic gel depends on the strain rate, values reported here are valid only at a strain rate of 0.2 s−1. After compression, the required stress to maintain a constant strain of 0.2 s−1, continuously decreases with time, which is a clear indication of the viscoelastic nature of the hydrogels and called stress relaxation. The shape of the stress relaxation curve was mathematically modelled with a generalized Maxwell model (2) (Fig. 1C). The continuously changing stress [σ(t)] was converted into continuously changing stiffness [E(t)] by dividing with the constant strain of 0.2 s−1. Obtained E(t) values were fitted to Eq. 1 to obtain the relaxation time constants (τi), and Eq. 2 provided relative importance (Ri) for each Maxwell element. Young's modulus essentially describes the stiffness of a material [30]. Since the modulus of the viscoelastic gel depends on the strain rate, values reported here are va at a strain rate of 0.2 s−1. After compression, the required stress to maintain a constant strain of continuously decreases with time, which is a clear indication of the viscoelastic natur hydrogels and called stress relaxation. The shape of the stress relaxation cur mathematically modelled with a generalized Maxwell model (2) (Fig. 1C). The conti changing stress [σ(t)] was converted into continuously changing stiffness [E(t)] by with the constant strain of 0.2 s−1. Obtained E(t) values were fitted to Eq. 1 to ob relaxation time constants (τi), and Eq. 2 provided relative importance (Ri) for each M element. ( ) = 1 − / 1 + 2 − / 2 + 3 − / 3 + … − / (1) = 100. ∑ =1 (2) where i varies from 1 to 4 or from 1 to 3 when necessary. The optimal number of M elements was determined with the chi-square function expressed by Eq. 3 (typically and visually matching the modelled stress relaxation curve to the measured curve (Fi 2 =∑ ( − ( ) ) 100 =0 (3) where j varies from 0 to 100 s, Ej is the experimentally measured value at time j, E(tj) value at time j calculated with Eq. 1, and σj is the standard error that the LLCT makes of inherent errors in position, time, and load measurements. (1) modulus of the viscoelastic gel depends on the strain rate, values reported here are v mathematically modelled with a generalized Maxwell model (2) (Fig. 1C). The cont i i − / − / − / − / =1 and visually matching the modelled stress relaxation curve to the measured curve (F − ( 100 =0 j j j (2) where i varies from 1 to 4 or from 1 to 3 when necessary. The optimal number of Maxwell elements was determined with the chi-square function expressed by Eq. 3 (typically 3 or 4) and visually matching the modelled stress relaxation curve to the measured curve (Fig. 1C). Young's modulus essentially describes the stiffness of a material [30]. Since the modulus of the viscoelastic gel depends on the strain rate, values reported here are va at a strain rate of 0.2 s−1. After compression, the required stress to maintain a constant strain of continuously decreases with time, which is a clear indication of the viscoelastic natur hydrogels and called stress relaxation. The shape of the stress relaxation cur mathematically modelled with a generalized Maxwell model (2) (Fig. 1C). The conti changing stress [σ(t)] was converted into continuously changing stiffness [E(t)] by with the constant strain of 0.2 s−1. Obtained E(t) values were fitted to Eq. 1 to ob relaxation time constants (τi), and Eq. 2 provided relative importance (Ri) for each M element. ( ) = 1 − / 1 + 2 − / 2 + 3 − / 3 + … − / (1) = 100. ∑ =1 (2) where i varies from 1 to 4 or from 1 to 3 when necessary. The optimal number of M elements was determined with the chi-square function expressed by Eq. 3 (typically and visually matching the modelled stress relaxation curve to the measured curve (Fi 2 =∑ ( − ( ) ) 100 =0 (3) where j varies from 0 to 100 s, Ej is the experimentally measured value at time j, E(tj) value at time j calculated with Eq. 1, and σj is the standard error that the LLCT makes of inherent errors in position, time, and load measurements. (3) 8
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